Image reconstruction performance

Summary

Statistics

These values are derived by using the aspect solution to 'de-dither' the ACA star images themselves. This process is done for every observation as part of the standard CXC Validation and Verification (V&V) process. In addition to a number of automatic aspect quality checks, a V&V scientist also inspects the plots by eye to check for any anomalies. Residuals after de-dithering the star come from both centroiding uncertainty and aspect solution uncertainty. The RMS deviation for a particular star thus gives an upper limit to the underlying aspect solution uncertainty. The plot below shows part of a sample V&V plot for one star.

The plot below shows a histogram (in black) of the 1-sigma residuals for each star in the 276 observations. For faint stars, centroiding uncertainty makes a large contribution. The red histogram shows the same value, but only for the 'best' (i.e. smallest 1-sigma residual) star in each observation. This gives a reasonable estimate of aspect solution uncertainty, which translates directly into image blurring during the image reconstruction process.

Analysis of a single observation

In addition to a statistical analysis of image reconstruction for many observations, we have also done a detailed analysis of a 50 ksec grating observation of a bright point source. A key motivation is to confirm, at least in one case, that the size of aspect deviations inferred from the V&V plot gives a firm upper limit to the true aspect error as seen in the reconstructed X-ray images. We initially looked for any aspect residuals by plotting the photon positions (in RA and Dec) as a function of time and looking for deviations from a constant. This yielded only upper limits -- the problem is that there are insufficient photons to get an accurate source centroid in a time small compared to the dither period.

Temporal phase binning

1. Convert the photon positions from sky coordinates (essentially RA and Dec) to spacecraft coordinates (i.e. lined up with the ACIS CCD axes). This means that photon position deviations (from the centroid) are in a coordinate system lined up with the dither axes. This is important because the dither frequency in yaw is different from the frequency in pitch.
2. Phase bin the data by modulating at an integral multiple of the dither period. In other words, for each photon arrival time, set
   
   T_bin = T_event MOD (N * T_dither)
   
   In this case we chose N=4. Choosing N>1 allows one to visually see any periodic residual in the data.

The plots below show the residuals for the 50 ksec observation. Any systematic residual due to aspect reconstruction would appear as a periodic deviation, with a period of 1 ksec for the top plot and 0.707 ksec for the bottom plot. The red line is a smoothed version of the photon positions, and no such deviation is visible.

In order to confirm the validity of this technique, we have purposely injected an error into the aspect solution and re-applied this aspect to the X-ray data. The error was induced by modifying the dark current map so as to produce a single "super-cold" pixel with a large negative offset. As the star dithers over the cold pixel, a periodic centroiding error is generated, which subsequenty produces a periodic error in the aspect solution. This is similar to the realistic situation when a star dithers over warm CCD pixels. (In this case we injected a unphysical cold pixel because the aspect pipeline automatically detects and compensates for warm pixels). The plot below now shows a clear periodic residual, the magnitude of which matches expectation based on the injected error signal and the 1-sigma deviation in the aspect V&V plot.

Spatial phase binning

Another way to detect an aspect residual is to bin the photon data spatially, based on spacecraft dither position. For this observation, the 16x16 arcsecond dither region was broken into a 7x7 square grid. For each of the 7x7 grid regions, an X-ray image was created with photons collected while the spacecraft was dithering through that region. The source centroid for each region was calculated and a vector offset from the mean centroid was determined. The set of vector offsets versus grid position is plotted below. This technique will again highlight systematic errors which are dependent on dither phase. It is apparent that there are no systematic trends in centroid offset as a function of dither position.

The vector offsets versus grid position for modified data (with an injected aspect error) are shown below. There is a clear systematic offset which is due to the "cold" pixel.